fence is to be built to enclose a rectangular area of 200 square feet. The fence along three sides is to be made of material that costs 4 dollars per foot, nd the material for the fourth side costs 16 dollars per foot. Find the dimensions of the enclosure that is most economical to construct. lint: Part 1: State the cost of the perimeter of this rectangle as a function of x and y. Note: make one of the 'x' sides to be the expensive one. C(2, y) =[] Part 2: State the area of this rectangle as a function of x and y. Part 3: Find y as a function of x, using the given value of the area of the rectangle. Part 4: Rewrite the cost as a function of x. Part 5: Find the derivative of the cost of the perimeter of the rectangle with respect to x. Part 6: Find the x and y values that minimize the cost of the perimeter of the rectangular fence.
fence is to be built to enclose a rectangular area of 200 square feet. The fence along three sides is to be made of material that costs 4 dollars per foot, nd the material for the fourth side costs 16 dollars per foot. Find the dimensions of the enclosure that is most economical to construct. lint: Part 1: State the cost of the perimeter of this rectangle as a function of x and y. Note: make one of the 'x' sides to be the expensive one. C(2, y) =[] Part 2: State the area of this rectangle as a function of x and y. Part 3: Find y as a function of x, using the given value of the area of the rectangle. Part 4: Rewrite the cost as a function of x. Part 5: Find the derivative of the cost of the perimeter of the rectangle with respect to x. Part 6: Find the x and y values that minimize the cost of the perimeter of the rectangular fence.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please circle the answer to each part thank
You
Transcribed Image Text:A fence is to be built to enclose a rectangular area of 200 square feet. The fence along three sides is to be made of material that costs 4 dollars per foot,
and the material for the fourth side costs 16 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
Hint:
Part 1: State the cost of the perimeter of this rectangle as a function of x and y. Note: make one of the 'x' sides to be the expensive one.
C(x, y) =
Part 2: State the area of this rectangle as a function of x and y.
Part 3: Find y as a function of x, using the given value of the area of the rectangle.
Part 4: Rewrite the cost as a function of x.
Part 5: Find the derivative of the cost of the perimeter of the rectangle with respect to x.
Part 6: Find the x and y values that minimize the cost of the perimeter of the rectangular fence.
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